Question

The radius of the base of a cone is $14cm$ and its height is $24cm$. Find the volume, curved surface area and total surface area of the cone.

Answer 1

Step 1: Find the slant height of the cone.

Given,

The radius of the base of a cone $r=14cm$

Height of the cone $h=24cm$

According to Pythagoras theorem, The slant height of cone $l=\sqrt{r^2+h^2}$

$\Rightarrow l=\sqrt{{14}^2+{24}^2}$

$\Rightarrow l=\sqrt{196+576}$

$\Rightarrow l=\sqrt{772}$

$\Rightarrow l=27.78cm$

Step 2: Find the volume of the cone.

Volume of the cone $V=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$, where $r$ is radius and $h$ is height

$V=\frac{1}{3}\times \frac{22}{7}\times {\left(14\right)}^2\times 24$ $\left(\because \mathrm{\pi }=\frac{22}{7}\right)$

$V=22\times 14\times 2\times 8$

$V=4928c{m}^3$

$\therefore$ Volume of the cone is $4928c{m}^3$.

Step 3: Find the curved surface area (CSA) of the cone.

CSA of the cone $=\mathrm{\pi r}l$, where $r$ is radius and $l$ is slant height

$=\frac{22}{7}\times 14\times 27.78$

$=22\times 2\times 27.78$

$=1222.32c{m}^2$

$\therefore$ Curved surface area of the cone is $1222.32c{m}^2$.

Step 4: Find the total surface area (TSA) of the cone.

TSA of the cone $=\mathrm{\pi r}\left(l+r\right)$, where $r$ is radius and $l$ is slant height

$=\frac{22}{7}\times 14\times \left(27.78+14\right)$

$=22\times 2\times 41.78$

$=1838.32c{m}^2$

Hence, total surface area of the cone is $1838.32c{m}^2$.